# Mixed type simulation data generator for sparse CCA `GenerateData` is used to generate two sets of data of mixed types for sparse CCA under the Gaussian copula model. ```r GenerateData( n, trueidx1, trueidx2, Sigma1, Sigma2, maxcancor, copula1 = "no", copula2 = "no", type1 = "continuous", type2 = "continuous", muZ = NULL, c1 = NULL, c2 = NULL ) ``` ## Arguments - `n`: Sample size - `trueidx1`: True canonical direction of length p1 for `X1`. It will be automatically normalized such that $w_1^T \Sigma_1 w_1 = 1$. - `trueidx2`: True canonical direction of length p2 for `X2`. It will be automatically normalized such that $w_2^T \Sigma_2 w_2 = 1$. - `Sigma1`: True correlation matrix of latent variable `Z1` (p1 by p1). - `Sigma2`: True correlation matrix of latent variable `Z2` (p2 by p2). - `maxcancor`: True canonical correlation between `Z1` and `Z2`. - `copula1`: Copula type for the first dataset. U1 = f(Z1), which could be either "exp", "cube". - `copula2`: Copula type for the second dataset. U2 = f(Z2), which could be either "exp", "cube". - `type1`: Type of the first dataset `X1`. Could be "continuous", "trunc" or "binary". - `type2`: Type of the second dataset `X2`. Could be "continuous", "trunc" or "binary". - `muZ`: Mean of latent multivariate normal. - `c1`: Constant threshold for `X1` needed for "trunc" and "binary" data type - the default is NULL. - `c2`: Constant threshold for `X2` needed for "trunc" and "binary" data type - the default is NULL. ## Returns `GenerateData` returns a list containing * Z1: latent numeric data matrix (n by p1). * Z2: latent numeric data matrix (n by p2). * X1: observed numeric data matrix (n by p1). * X2: observed numeric data matrix (n by p2). * true_w1: normalized true canonical direction of length p1 for `X1`. * true_w2: normalized true canonical direction of length p2 for `X2`. * type: a vector containing types of two datasets. * maxcancor: true canonical correlation between `Z1` and `Z2`. * c1: constant threshold for `X1` for "trunc" and "binary" data type. * c2: constant threshold for `X2` for "trunc" and "binary" data type. * Sigma: true latent correlation matrix of `Z1` and `Z2` ((p1+p2) by (p1+p2)). ## Examples ```r ### Simple example # Data setting n <- 100; p1 <- 15; p2 <- 10 # sample size and dimensions for two datasets. maxcancor <- 0.9 # true canonical correlation # Correlation structure within each data set set.seed(0) perm1 <- sample(1:p1, size = p1); Sigma1 <- autocor(p1, 0.7)[perm1, perm1] blockind <- sample(1:3, size = p2, replace = TRUE); Sigma2 <- blockcor(blockind, 0.7) mu <- rbinom(p1+p2, 1, 0.5) # true variable indices for each dataset trueidx1 <- c(rep(1, 3), rep(0, p1-3)) trueidx2 <- c(rep(1, 2), rep(0, p2-2)) # Data generation simdata <- GenerateData(n=n, trueidx1 = trueidx1, trueidx2 = trueidx2, maxcancor = maxcancor, Sigma1 = Sigma1, Sigma2 = Sigma2, copula1 = "exp", copula2 = "cube", muZ = mu, type1 = "trunc", type2 = "trunc", c1 = rep(1, p1), c2 = rep(0, p2) ) X1 <- simdata$X1 X2 <- simdata$X2 # Check the range of truncation levels of variables range(colMeans(X1 == 0)) range(colMeans(X2 == 0)) ```

GenerateData function